SOLUTION: the length of a shadow cast by a sundial with a 3 foot tall gnomon is given by I(0) = 3 cot 0, where 0 is the angle of the sun above the eastern horizon. (0�&#8804;0&#8804; 180�)

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Question 1111358: the length of a shadow cast by a sundial with a 3 foot tall gnomon is given by I(0) = 3 cot 0, where 0 is the angle of the sun above the eastern horizon. (0�≤0≤ 180�)
a. sketch a graph for the function.
b. identify the asymptotes and interpret what they represent in th contex of the problem.
c. for what values of 0 does the rod cast a 3 foot shadow?
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
The cotangent is undefined at 0 degrees
The shadow is infinitely long at 0 degrees (sun is at horizon) and at 180 degrees.
It casts a 3 foot shadow at 45 and 135 degrees, because cot x= tan x=1
It casts no shadow at 90 degrees (local noon), because at least this design will have the sun highest in the sky (90 degrees from horizon). Note: this has to be a special kind of sundial, since the sun is directly overhead and casting no shadow only at certain time of year between the Tropics of Cancer and Capricorn.
The cotangent function is the tangent shifted 90 degrees, the way the sine and cosine functions are shifted.

SOLUTION: the length of a shadow cast by a sundial with a 3 foot tall gnomon is given by I(0) = 3 cot 0, where 0 is the angle of the sun above the eastern horizon. (0�&#8804;0&#8804; 180�)

SOLUTION: the length of a shadow cast by a sundial with a 3 foot tall gnomon is given by I(0) = 3 cot 0, where 0 is the angle of the sun above the eastern horizon. (0�≤0≤ 180�)